Probing the structural evolution of ruthenium doped germanium clusters: Photoelectron spectroscopy and density functional theory calculations

Magnetic properties of CrMnGen (n = 3-20) clusters

Due to the potential applications in next-generation micro/nano electronic devices and functional materials, magnetic germanium (Ge)-based clusters are receiving increasing attention. In this work, we reported the structures, electronic and magnetic properties of CrMnGen with sizes n = 3-20. Transition metals (TMs) of Cr and Mn tend to stay together and be surrounded by Ge atoms. Small sized clusters with n ≤ 8 prefer to adopt bipyramid-based structures as the motifs with the excess Ge atoms absorbed on the surface. Starting from n = 9, the structure with one TM atom interior appears and persists until n = 16, and for larger sizes n = 17-20, the two TM atoms are full-encapsulated by Ge atoms to form endohedral structures. The Hirshfeld population analyses show that Cr atom always acts as the electron donor, while Mn atom is always the acceptor except for sizes 3 and 6. The average binding energies of these clusters increase with cluster size n, sharing a very similar trend as that of CrMnSin (n = 4-20) clusters, which indicates that it is favorable to form large-sized clusters. CrMnGen (n = 6, 13, 16, 19, and 20) clusters prefer to exhibit ferromagnetic Cr-Mn coupling, while the remaining clusters are ferrimagnetic.

Aromatic and magnetic properties in a series of heavy rare earth-doped Ge6 cluster anions

A series of pentagonal bipyramidal anionic germanium clusters doped with heavy rare earth elements,REGe 6 - (RE = Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu), have been identified at the PBE0/def2-TZVP level using density functional theory (DFT). Our findings reveal that the centrally doped pentagonal ring structure demonstrates enhanced stability and heightened aromaticity due to its uniform bonding characteristics and a larger charge transfer region. Through natural population analysis and spin density diagrams, we observed a monotonic decrease in the magnetic moment from Gd to Yb. This is attributed to the decreasing number of unpaired electrons in the 4f orbitals of the heavy rare earth atoms. Interestingly, the system doped with Er atoms showed lower stability and anti-aromaticity, likely due to the involvement of the 4f orbitals in bonding. Conversely, the systems doped with Gd and Tb atoms stood out for their high magnetism and stability, making them potential building blocks for rare earth-doped semiconductor materials.

Cr2 Gen - (n = 15-20) clusters with two Cr atoms exhibited antiferromagnetic coupling

In this work, we investigated the structural evolution, electronic and magnetic properties of Cr₂ Ge_n ^- clusters for n = 15-20 by using density functional theory (DFT) calculations. Low-energy structures for these clusters were fully searched through a self-developed genetic algorithm code combined with DFT calculations. The calculations show that all the two Cr atoms prefer to stay together to form a strong CrCr bond, which-except for size 20-is shorter than the nearest neighbor distance in Cr bulk. Sizes 15 and 16 adopt a wheel-like structure as the structural motif with the extra Ge atoms capped on the top, while larger sizes (n = 17-20) prefer fullerene-like Cr₂ @Ge₁₂ motifs. From the results of the average binding energies of Cr₂ Ge_n ^- , one can conclude that it is easier to form larger size clusters. In these lowest-lying isomers except for size 16, the two Cr atoms contribute opposite magnetic moments for the total magnetic moments of 1 μ_B , showing an antiferromagnetic state.

First-row transition metal doped germanium clusters Ge16M: some remarkable superhalogens

A theoretical study of geometric and electronic structures, stability and magnetic properties of both neutral and anionic Ge16M0/- clusters with M being a first-row 3d transition metal atom, is performed using quantum chemical approaches. Both the isoelectronic Ge16Sc- anion and neutral Ge16Ti that have a perfect Frank-Kasper tetrahedral T d shape and an electron shell filled with 68 valence electrons, emerge as magic clusters with an enhanced thermodynamic stability. The latter can be rationalized by the simple Jellium model. Geometric distortions from the Frank-Kasper tetrahedron of Ge16M having more or less than 68 valence electrons can be understood by a Jahn-Teller effect. Remarkably, DFT calculations reveal that both neutral Ge16Sc and Ge16Cu can be considered as superhalogens as their electron affinities (≥3.6 eV) exceed the value of the halogen atoms and even that of icosahedral Al13. A detailed view of the magnetic behavior of Ge16M0/- clusters shows that the magnetic moments of the atomic metals remain large even when they are quenched upon doping. When M goes from Sc to Zn, the total spin magnetic moment of Ge16M0/- increases steadily and reaches the maximum value of 3 μ B with M = Mn before decreasing towards the end of the first-row 3d block metals. Furthermore, the IR spectra of some tetrahedral Ge16M are also predicted.

A joint experimental and theoretical study on structural, electronic, and magnetic properties of MnGen - (n = 3-14) clusters

A systematic structure and property investigation of MnGe_n ^- (n = 3-14) was conducted by means of density functional theory coupled with mass-selected anion photoelectron spectroscopy. This combined theoretical and experimental study allows global minimum and coexistence structures to be identified. It is found that the pentagonal bipyramid shape is the basic framework for the nascent growth process of MnGe_n ^- (n = 3-10), and from n = 10, the endohedral structures can be found. For n = 12, the anion MnGe₁₂ ^- cluster probably includes two isomers: a major isomer with a puckered hexagonal prism geometry and a minor isomer with a distorted icosahedron geometry. Specifically, the puckered hexagonal prism isomer follows the Wade-Mingos rules and can be suggested as a new kind of superatom with the magnetic property. Furthermore, the results of adaptive natural density partitioning and deformation density analyses suggest a polar covalent interaction between Ge and Mn for endohedral clusters of MnGe₁₂ ^-. The spin density and natural population analysis indicate that MnGe_n ^- clusters have high magnetic moments localized on Mn. The density of states diagram visually shows the significant spin polarization for endohedral structures and reveals the weak interaction between the Ge 4p orbital and the 4s, 3d orbitals of Mn.

New potential stable structures of XMg n (X = Ge, C, Sn; n = 2-12) clusters: XMg8 with high stability

Several potential stable structures of X-doped magnesium (X = Ge, C, Sn) clusters have been fully investigated by using CALYPSO structure searching software together with density functional theory calculations. XMg _n (X = Ge, C, Sn; n = 3-7) clusters have similar geometric structure grows in tetrahedron, while the structures of XMg _n (X = Ge, C, Sn; n = 8-12) are based on a kind of tower-like geometry. Interestingly, the relative stability computations indicate that XMg₈ (X = Ge, C, Sn) are more stable than other clusters, and thus can be identified as magic clusters. In addition, XMg₈'s (X = Ge, C, Sn) high stability and atomic interactions contained in structures are studied through their electronic localization function and molecular orbitals. It is shown that the covalent σ bond interaction of X-Mg and Mg-Mg are mainly responsible for their robust stability. Finally, the theoretical calculations of IR and Raman spectra of XMg₈ (X = Ge, C, Sn) clusters were implemented for guiding further experimental observation.

Identification of octahedral coordinated ZrN12+ cationic clusters by mass spectrometry and structure searches

Cationic zirconium-doped nitrogen clusters were produced by laser ablation of a Zr : BN mixture target and were detected by TOF mass spectrometry. It is found that the mass peak of the ZrN12+ cluster is dominant in the spectrum. The ZrN12+ cluster was further dissociated with 266 nm photons. Extensive structure searches of a cationic ZrN12+ cluster indicate that the ground state structure of ZrN12+ consists of a central Zr atom and six N2 pairs with Oh symmetry. The calculated binding energy of the ZrN12+ cluster is about 0.96 eV, which is in accordance with the result of the photodissociation experiment. The neutral ZrN12 cluster has almost the same geometry, but with D3h symmetry. NBO analysis showed that the molecular orbitals of ZrN12+/0 clusters are mainly composed of Zr 4d and N 2p orbitals. These findings provide rich information for understanding the geometries and the electronic properties of zirconium-doped N clusters, which will offer valuable guidance for the exploration of other metal doped nitrogen clusters.

Energetic degeneracy and electronic structures of germanium trimers doped with titanium

Geometries and electronic structures of germanium trimer clusters doped with titanium TiGe₃ ^-/0 were studied making use of the complete active space self-consistent field followed by second-order perturbation theory explicitly correlated coupled cluster singles and doubles method with perturbative triples corrections CCSD(T)-F12 and Tao-Perdew-Staroverov-Scuseria methods. Two electronic states (²A' and ²A″) of the anion (pyramid shape) were determined to be nearly degenerate and energetically competing for the anionic ground state of TiGe₃ ^-. These two anionic states are believed to be concurrently populated in the experiment and induce six observed anion photoelectron bands. Total 14 electronic transitions starting from the ²A' and ²A″ states were assigned to five out of six visible bands in the experimental anion photoelectron spectrum of TiGe₃ ^-. Each band was proven to be caused by multiple one-electron detachments from two populated anionic states. The last experimental band with the highest detachment energy is believed to be the result of various inner one-electron removals.

Probing the structural evolution and electronic properties of divalent metal Be2Mgn clusters from small to medium-size

Bimetallic clusters have aroused increased attention because of the ability to tune their own properties by changing size, shape, and doping. In present work, a structural search of the global minimum for divalent bimetal Be₂Mg_n (n = 1-20) clusters are performed by utilizing CALYPSO structural searching method with subsequent DFT optimization. We investigate the evolution of geometries, electronic properties, and nature of bonding from small to medium-sized clusters. It is found that the structural transition from hollow 3D structures to filled cage-like frameworks emerges at n = 10 for Be₂Mg_n clusters, which is obviously earlier than that of Mg_n clusters. The Be atoms prefer the surface sites in small cluster size, then one Be atom tend to embed itself inside the magnesium motif. At the number of Mg larger than eighteen, two Be atoms have been completely encapsulated by caged magnesium frameworks. In all Be₂Mg_n clusters, the partial charge transfer from Mg to Be takes place. An increase in the occupations of the Be-2p and Mg-3p orbitals reveals the increasing metallic behavior of Be₂Mg_n clusters. The analysis of stability shows that the cluster stability can be enhanced by Be atoms doping and the Be₂Mg₈ cluster possesses robust stability across the cluster size range of n = 1-20. There is s-p hybridization between the Be and Mg atoms leading to stronger Be-Mg bonds in Be₂Mg₈ cluster. This finding is supported by the multi-center bonds and Mayer bond order analysis.

Structural evolution and magnetic properties of anionic clusters Cr2Ge n (n = 3-14): photoelectron spectroscopy and density functional theory computation

The structural, electronic and magnetic properties of dual Cr atoms doped germanium anionic clusters, [Formula: see text] (n  =  3-14), have been investigated by using photoelectron spectroscopy in combination with density-functional theory calculations. The low-lying structures of [Formula: see text] are determined by DFT based genetic algorithm optimization. For [Formula: see text] with n  ⩽  8, the structures are bipyramid-based geometries, while [Formula: see text] cluster has an opening cage-like structure, and the half-encapsulated structure is gradually covered by the additional Ge atoms to form closed-cage configuration with one Cr atom interior for n  =  10 to 14. Meanwhile, the two Cr atoms in [Formula: see text] clusters tend to form a Cr-Cr bond rather than be separated. Interestingly, the magnetic moment of all the anionic clusters considered is 1 μ _B. Almost all clusters exhibit antiferromagnetic Cr-Cr coupling, except for two clusters, [Formula: see text] and [Formula: see text]. To our knowledge, the [Formula: see text] cluster is the first kind of transition-metal doped semiconductor clusters that exhibit relatively stable antiferromagnetism within a wide size range. The experimental/theoretical results suggest high potential to modify the magnetic behavior of semiconductor clusters through introducing different transition-metal dopant atoms.

Structural and magnetic properties of FeGen-/0 (n = 3-12) clusters: Mass-selected anion photoelectron spectroscopy and density functional theory calculations

The structural, electronic, and magnetic properties of FeGe_n^-/0 (n = 3-12) clusters were investigated by using anion photoelectron spectroscopy in combination with density functional theory calculations. For both anionic and neutral FeGe_n (n = 3-12) clusters with n ≤ 7, the dominant structures are exohedral. The FeGe₈^-/0 clusters have half-encapsulated boat-shaped structures, and the opening of the boat-shaped structure is gradually covered by the additional Ge atoms to form Ge_n cage from n = 9 to 11. The structures of FeGe₁₀^-/0 can be viewed as two Ge atoms symmetrically capping the opening of the boat-shaped structure of FeGe₈, and those of FeGe₁₂^-/0 are distorted hexagonal prisms with the Fe atom at the center. Natural population analysis shows that there is an electron transfer from the Ge atoms to the Fe atom at n = 8-12. The total magnetic moment of FeGe_n^-/0 and local magnetic moment of the Fe atom have not been quenched.

Probing the Structural and Electronic Properties of Dirhenium Halide Clusters: A Density Functional Theory Study

Dirhenium halide dianions received considerable attention in past decades due to the unusual metal-metal quadruple bond. The systematic structural evolution of dirhenium halide clusters has not been sufficiently studied and hence is not well-understood. In this work, we report an in-depth investigation on the structures and electronic properties of doubly charged dirhenium halide clusters Re₂X₈^2- (X = F, Cl, Br, I). Our computational efforts rely on the well-tested unbiased CALYPSO (Crystal structure AnaLYsis by Particle Swarm Optimization) method combined with density functional theory calculations. We find that all ground-state Re₂X₈^2- clusters have cube-like structures of D_4h symmetry with two Re atoms encapsulated in halogen framework. The reasonable agreement between the simulated and experimental photoelectron spectrum of the Re₂Cl₈^2- cluster supports strongly the reliability of our computational strategy. The chemical bonding analysis reveals that the δ bond is the pivotal factor for the ground-state Re₂X₈^2- (X = F, Cl, Br, I) clusters to maintain D_4h symmetric cube-like structures, and the enhanced stability of Re₂Cl₈^2- is mainly attributed to the chemical bonding of 5d orbital of Re atoms and 3p orbital of Cl atoms.

First-principle study of structural, electronic and magnetic properties of (FeC)n (n = 1-8) and (FeC)8TM (TM = V, Cr, Mn and Co) clusters

The structural, electronic and magnetic properties of the (FeC)_n (n = 1–8) clusters are studied using the unbiased CALYPSO structure search method and density functional theory. A combination of the PBE functional and 6–311 + G* basis set is used for determining global minima on potential energy surfaces of (FeC)_n clusters. Relatively stabilities are analyzed via computing their binding energies, second order difference and HOMO-LUMO gaps. In addition, the origin of magnetic properties, spin density and density of states are discussed in detail, respectively. At last, based on the same computational method, the structures, magnetic properties and density of states are systemically investigated for the 3d (V, Cr, Mn and Co) atom doped (FeC)₈ cluster.

Insights into Geometric and Electronic Structures of VGe3-/0 Clusters from Anion Photoelectron Spectrum Assignment

The global minima of both neutral and anionic clusters of VGe₃^-/0 were determined using different quantum chemical methods (DFT, RCCSD(T), CASSCF/CASPT2). On the basis of the ground states identified, most excited bands in the anion photoelectron spectrum of VGe₃^- were assigned. The tetrahedral isomers of both charged states are the most stable ones. A singlet state (C_s^, 1A') of the tetrahedral isomer has the globally lowest energy on the potential hypersurface of VGe₃^-. Two states 1²A' and 1²A″ of the neutral tetrahedral isomer are nearly degenerate and identified as the competing ground state of VGe₃. From the anionic ground state, four of five bands in the anion photoelectron spectrum of VGe₃^- were determined to be the consequences of one-electron transitions starting from the anionic ground state ¹A'. Both nearly degenerate neutral ground states are responsible for generation of the first band. Two different transitions from the anionic ground state ¹A' to the first two nearly degenerate excited states (2²A' and 2²A″) of the neutral underlie the second lowest ionization band. Two higher levels of ionization recorded in the spectrum were assigned to the two higher excited states 4²A' and 5²A' of the neutral. Franck-Condon factor simulations of the first band were performed to obtain more insights into the experimental bands of the spectrum.

Insights into the structures and electronic properties of Cun+1μ and CunS μ (n = 1-12; μ = 0, ±1) clusters

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The stability and reactivity of clusters are closely related to their valence electronic configuration. Doping is a most efficient method to modify the electronic configuration and properties of a cluster. Considering that Cu and S posses one and six valence electrons, respectively, the S doped Cu clusters with even number of valence electrons are expected to be more stable than those with odd number of electrons. By using the swarm intelligence based CALYPSO method on crystal structural prediction, we have explored the structures of neutral and charged Cu_n+1 and Cu_nS (n = 1-12) clusters. The electronic properties of the lowest energy structures have been investigated systemically by first-principles calculations with density functional theory. The results showed that the clusters with a valence count of 2, 8 and 12 appear to be magic numbers with enhanced stability. In addition, several geometry-related-properties have been discussed and compared with those results available in the literature.

Titanium Digermanium: Theoretical Assignment of Electronic Transitions Underlying Its Anion Photoelectron Spectrum

Electronic structures of both the anionic and neutral triatomic species TiGe₂^-/0 were theoretically studied employing single-reference (DFT and RCCSD(T)) and multiconfigurational (CASSCF/CASPT2 and CASSCF/NEVPT2) methods with large basis sets. The ground state of TiGe₂^- (C_2v) was identified to be ⁴B₁, but the ²A₁ state is nearly degenerate, whereas the ³B₁ is clearly the ground state of the neutral TiGe₂ (C_2v). On the basis of the computed ground and excited states of both neutral and anionic structures, all electronic transitions giving rise to experimental anion photoelectron bands in the spectrum of TiGe₂^- can now be assigned. The X band of the anion photoelectron spectrum is attributed to a one-electron transition between two ground states ⁴B₁ → ³B₁. Three neutral excited states 2³A₂, 2⁵B₁, and 3⁵B₁ are energetically responsible for the B band upon one-electron photodetachement from the anionic ground state ⁴B₁. The C band is assigned to the transition ⁴B₁ → 2⁵A₁. A transition from the nearly degenerate ground state ²A₁ of the anion to the low-spin ¹A₁ of the final neutral state can be ascribed to the A band. Furthermore, the first two bands' progressions, whose normal vibrational modes were accessible from CASSCF/CASPT2 calculations, were also simulated by determination of multidimensional Franck-Condon factors.

New insight into the structural evolution of PbTiO3: an unbiased structure search

Understanding the structural evolution of materials is a challenging problem of condensed matter physics. Solving this problem would open new ways for understanding the behaviors of materials. In this context, we here report unbiased structure searches for a prototypical perovskite oxide, PbTiO₃, based on the CALYPSO (Crystal structure AnaLYsis by Particle Swarm Optimization) method in conjunction with first-principles calculations. For the first time, we decipher the structure evolution of PbTiO₃ from a zero dimensional (0D) cluster to a two dimensional (2D) layered structure and in the end to a three dimensional (3D) bulk solid. Our unbiased structure search is successful in reproducing the cubic Pm3[combining macron]m and tetragonal P4mm phases of PbTiO₃ at ambient pressure. We also predict a new quasi-planar kite shape structure of the PbTiO₃ cluster, with C_s symmetry and a surprisingly large HOMO-LUMO gap. Furthermore, by using this method, we predict that the 2D planar PbTiO₃ monolayer is unstable in the perpendicular direction and the 2D PbTiO₃ double layer is dynamically stable, with a hope that it can provide guidance to future synthesis of low dimensional perovskite oxides.